The victim, Kelly Phillips, and the suspect, Lyle "Ty" Hoffman, together opened Lush Food Bar in 2009.

For more than a decade, Kelly Phillips and Lyle “Ty” Hoffman had a personal and professional relationship.

On Monday morning, long after both had soured, Phillips, a 48-year-old executive with Boston Scientific, lay dead on the pavement of an Arden Hills gas station and Hoffman was on the run, identified by police as a suspect in the slaying.

Authorities didn’t say Tuesday why Hoffman, a 44-year-old commercial developer, is suspected in the gruesome shooting death. He and Phillips had operated Minneapolis nightspot Lush Food Bar together, and they had lived together up until about three years ago.

In 2009, Hoffman and Phillips opened Lush, a popular Northeast gay bar. Friends said Hoffman worked at the bar, while Phillips’ involvement was financial. The bar was closed ­Tuesday.

As of Tuesday night, no one had been arrested and Hoffman’s whereabouts were unknown.

Earlier in the day, police swarmed an area near the Anoka County-Blaine airport, not far from where authorities found the BMW driven by the man who shot Phillips.

Authorities searched the two hangars, believing that Hoffman may have slept inside one of them because he was familiar with the area and knew how to get inside at least one of the buildings.

They also searched the area where the BMW was found just outside the airport, next to a golf course. Authorities did not find the gun in either of those searches, they said Tuesday night.

Working off the theory that Hoffman may have been the killer, investigators Tuesday were busy trying to figure out what brought him and Phillips together Monday morning, and whether Hoffman may have caught Phillips by surprise, a Ramsey County law enforcement official said.

Phillips was shot in the back and head about 8:40 a.m. Monday.

Police said both men were in the BMW in a Holiday station parking lot on County Road 96 near Interstate 35W.

Josh Polos, who was filling his tank with gas at the Holiday station when the BMW pulled up behind him Monday morning, witnessed the killing.

Polos said he heard yelling in the car and assumed it was directed at him.

But when he got out, the car passed his SUV and pulled into a parking spot next to the station. As Polos watched, two men got out of the car and the driver shot the other man three times — including in the back as the victim started running, and finally in the head from close range as the wounded man pleaded for his life.

The shooter turned to Polos and looked him full in the face. He then got back into the car, sat there for several seconds and sped away — running over the Phillips as he left.

“It was so surreal,” Polos said afterward. “You’d think that you’d run, but I just stood there, frozen like a deer in headlights.”

Troubled relationship

Kathy Simon, who was married to Phillips until about 20 years ago and remained close to him, said Tuesday that she had seen Hoffman many times over the years, describing him as “a very nice guy … kind of fun.”

But later, she said, the relationship turned stormy as Phillips said Hoffman was becoming “resentful, bitter, even kind of desperate.”

Phillips once told Simon that “Ty was sort of violent and that he was ending the relationship.”

She added: “I looked him straight in the eye and said, ‘Get a lawyer, you know how this works. Take some steps.’ ”

Since the breakup about three years ago, she said, “there were money [conflicts], and things were getting a little crazy, it seemed,” referring to the bar they started together five years ago.